Each class has a role that defines where it fits in the adventuring party. Here is a rundown of party roles:

Leader
Striker
Defender
Controller

Each class has a primary role and one of two secondary roles depending on things like race, power choices, feat choices, etc.

For a party of 5 one should try to have one of each and then either double up on striker or defender depending on play style and secondary roles.

Defenders have two goals - either be the one taking the damage and be able to survive it, or make it very unattractive for the DM to attack anyone but you. There are currently four defenders available.

Fighters are the basic defender type. They can "mark" an enemy and then get free attacks if that enemy tries to leave the fighter - and even hold them in place in some instances. Depending on style, Fighters can be made into good secondary strikers or secondary strikers, depending on whether you want to focus on doing damage or doing more damage. There is an essence of controller and leader in there as well, but not to the extent of the other defenders.

Paladins haven't really changed much. They are still primarily defenders, and can "mark" enemies with a divine challenge that automatically damages them if they ignore you and decide to go for the squishies. They can heal a bit and have characteristics of either a leader or striker secondary. Paladins make better secondary leaders than the other defenders.

Swordmages, while not technically core (Forgotten Realms) have been elevated to core status in my opinion with their inclusion in the Arcane Power source book. Swordmages are arcane defenders, and feature a steep learning curve because they function better when moving about the battlefield. Their marks allow the swordmage to do various things if enemies attack allies - either teleport next to the enemy and attack for free, reduce any damage dealt to allies from said attack, or even teleport the enemy to the swordmage. A bit more vurnerable than the other defenders, Swordmages allow for the most customizable defender and make excellent 5th characters.

Wardens are sort of a druid-in-fighter's-clothing. They can mark enemies and then if that enemy chooses to attack an ally you can either move them and cripple their speed or damage them and make them flat footed. They boast high hit points and AC, and can pull off a controller secondary better than the other two, but will also make a viable striker secondary.

Strikers are the backbone of the party. They are the ones putting up the big numbers and keeping battles from being attrition wars. They come in all shapes and sizes, and are the most varied role. Strikers are all pretty one dimensional in combat, but each one retains it's old school feel out of combat, such as rangers with wilderness abilities, and rogues with thievery.

Rangers are arguably the most versatile striker class. They can fight with two weapons or a bow (but not both, at least not very well) and pound out the damage at higher levels. At lower levels they focus on solid damage to two enemies at a time. They can mark one enemy to receive extra damage from attacks.

Rogues can dish out *huge* damage to a single enemy at a time, but with the caveat that they need combat advantage (flanking, hidden, etc.) They have plenty of unique ways to get this, and a good rogue should always be doing sneak attack/backstabbing damage.

Warlocks are very customizable. You can go balls to the wall assault magic, go with crippling spells that damage and weaken, a controller-like warlock that damages and manipulates, or go for a more defender-like warlock and buff yourself up as you damage them. Or some combination of the four. They tend to require a bit more pre-game planning, but the rewards are equally high.

Avengers are cool in that they can single out a target and as long as no other enemy is adjacent to you, you may roll twice and choose the better attack. Most of your powers focus on either chasing down or isolating your target. Avengers may not put up the numbers of the other strikes in terms of damage, but their damage will be more consistent.

Barbarians haven't changed much. They still rage, still produce sickening amounts of damage, still take a hell of a beating (compared to non-defenders at least), and still have only two settings: ridiculous and wtf just happened. There is no doubt that barbarians can put up the highest numbers in a single turn if they blow everything, but you must ration your rages and abilities to avoid becoming an exhausted wimp.

Sorcerers underwent a huge change in 4e. They are now focused entirely on covering the battlefield in destruction. This is done either up close with large area effects and personal buffs, or from afar with single target crippling spells. They have a slight controller bend to them, and can substitute for one in a pinch if needed. Tends to put out slightly lower damage than the other strikers but to more targets, and with more crippling effects. Also tend to hit at an above average rate.

Leaders aren't really named right. They are more like supporters than actual party leaders, for anyone can be a party leader. Leaders don't have a common ground, nor is there any consistent purpose like defenders, strikers and controllers. Each one is different. Currently there are four leaders.

Clerics are no longer dedicated healers. Well, you can be if you want, but they are perfectly capable of launching a melee assault right along with the others, and even bolstering your allies in the process. Or you can hang a bit further back and focus on less damage output but more heals and buffs to your allies.

Warlords are a curious bunch. They are akin to Marshals from the D&D minis game, wading through melee right next to the defenders and actually giving your allies extra movement or even free attacks! You can forgo your attack completely and instead allow an ally to attack the enemy, adding your damage bonus. Warlords can quickly turn the tide of a battle by switching places with, moving, and granting bonuses to allies. Very tactical class, but requires a melee/martial heavy party to succeed.

Bards are no less complex than they were in 3e. They can do just about everything sort of well. Actually they can do everything at least at a pretty average pace. They can heal, buff, attack, cripple, control, sing, talk, and even mark enemies on behalf of allies! They also have more out of combat style than the other leaders.

Shaman is the pet class. They have a spirit companion that pretty much does their work for them. Similar to the bard in that they can be made to do just about anything reasonably well, with the pet being the focus. Very interesting class to play, and something that as far as I know is new to the D&D world.

Controllers do just that. They control the battlefield. This is most often done by moving and sliding enemies, and preventing the DM from being able to execute the tactical plan he has envisioned through various means. Each class accomplishes this a different way.

Wizards are still the masters of magic in and out of battle. They get the most abilities at first level, including standards like prestidigitation and ghost sound, and can perform rituals out of battle. In battle they focus on covering large swaths of the map with magic. It's not uncommon to see a wizard dole out minor damage to 5 or 6 enemies at once, killing off minions and weakened foes. Or you could focus on crippling enemies movement and attacks. Wizards also have abilities to create lingering effects like gas clouds and ice sheets.

Druids return much like they did before, with two distinct types. Shifters and casters. Depending on your style you will lean to either a striker or leader secondary. Druids have the unique ability to exert full controller potential at a melee range while wild shaped. They can also stand back and play wizard, including abilities that force the DM to choose between two bad options. Druids can make allies into defenders, freeing up defenders to fall into their secondary roles more readily.

Invokers are divine controllers. They feel more like strikers in that they don't produce the fancy effects that wizards and druids do. They do put out a consistent if small amount of damage to a large number of enemies, often including a status effects. Playing an invoker is the fastest way to make sure nearly every enemy in nearly every fight has some negative effect on it, and that no enemy lasts long with only a handful of hp remaining.